Let <i>G</i> be any compact connected Lie group and let <i>T</i> ≤ <i>G</i> be a maximal torus. Then for any unstable Adams operation <i>f</i> of degree <i>k</i>, the following diagram commutes up to homotopy «!» And conversely, any map <i>f</i> that makes the above diagram commute must be an unstable Adams operation. Using this characterization, we will construct a self-map of a <i>p</i>-local compact group (<i>S,F,L</i>) in order to define unstable Adams operations on a more general setting. THEOREM. For any <i>p</i>-local compact group (<i>S,F,L</i>) there is a self-equivalence such that the map on the objects when restricted to the identity component of <i>S</i> is a <i>q<sup>m</sup>-th </i>power map.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:531931 |
| Date | January 2008 |
| Creators | Junod, Fabien |
| Publisher | University of Aberdeen |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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